One's Complement: Binary -> Integer: 0111 1111 1111 1111 1111 1111 1111 1110 0010 1001 1000 0001 1001 0000 0100 1101 Signed Binary Number in One's Complement Representation, Converted and Written as a Decimal System Integer (in Base Ten)

Signed binary in one's complement representation 0111 1111 1111 1111 1111 1111 1111 1110 0010 1001 1000 0001 1001 0000 0100 1101(2) converted to an integer in decimal system (in base ten) = ?

1. Is this a positive or a negative number?

In a signed binary in one's complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.

0111 1111 1111 1111 1111 1111 1111 1110 0010 1001 1000 0001 1001 0000 0100 1101 is the binary representation of a positive integer, on 64 bits (8 Bytes).


2. Get the binary representation of the positive (unsigned) number.

* Run this step only if the number is negative *

Flip all the bits of the signed binary in one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:

* Not the case - the number is positive *


3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:

    • 263

      0

    • 262

      1

    • 261

      1

    • 260

      1

    • 259

      1

    • 258

      1

    • 257

      1

    • 256

      1

    • 255

      1

    • 254

      1

    • 253

      1

    • 252

      1

    • 251

      1

    • 250

      1

    • 249

      1

    • 248

      1

    • 247

      1

    • 246

      1

    • 245

      1

    • 244

      1

    • 243

      1

    • 242

      1

    • 241

      1

    • 240

      1

    • 239

      1

    • 238

      1

    • 237

      1

    • 236

      1

    • 235

      1

    • 234

      1

    • 233

      1

    • 232

      0

    • 231

      0

    • 230

      0

    • 229

      1

    • 228

      0

    • 227

      1

    • 226

      0

    • 225

      0

    • 224

      1

    • 223

      1

    • 222

      0

    • 221

      0

    • 220

      0

    • 219

      0

    • 218

      0

    • 217

      0

    • 216

      1

    • 215

      1

    • 214

      0

    • 213

      0

    • 212

      1

    • 211

      0

    • 210

      0

    • 29

      0

    • 28

      0

    • 27

      0

    • 26

      1

    • 25

      0

    • 24

      0

    • 23

      1

    • 22

      1

    • 21

      0

    • 20

      1

4. Multiply each bit by its corresponding power of 2 and add all the terms up.

0111 1111 1111 1111 1111 1111 1111 1110 0010 1001 1000 0001 1001 0000 0100 1101(2) =

(0 × 263 + 1 × 262 + 1 × 261 + 1 × 260 + 1 × 259 + 1 × 258 + 1 × 257 + 1 × 256 + 1 × 255 + 1 × 254 + 1 × 253 + 1 × 252 + 1 × 251 + 1 × 250 + 1 × 249 + 1 × 248 + 1 × 247 + 1 × 246 + 1 × 245 + 1 × 244 + 1 × 243 + 1 × 242 + 1 × 241 + 1 × 240 + 1 × 239 + 1 × 238 + 1 × 237 + 1 × 236 + 1 × 235 + 1 × 234 + 1 × 233 + 0 × 232 + 0 × 231 + 0 × 230 + 1 × 229 + 0 × 228 + 1 × 227 + 0 × 226 + 0 × 225 + 1 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 0 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 1 × 216 + 1 × 215 + 0 × 214 + 0 × 213 + 1 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 1 × 26 + 0 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =

(0 + 4 611 686 018 427 387 904 + 2 305 843 009 213 693 952 + 1 152 921 504 606 846 976 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 72 057 594 037 927 936 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 9 007 199 254 740 992 + 4 503 599 627 370 496 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 562 949 953 421 312 + 281 474 976 710 656 + 140 737 488 355 328 + 70 368 744 177 664 + 35 184 372 088 832 + 17 592 186 044 416 + 8 796 093 022 208 + 4 398 046 511 104 + 2 199 023 255 552 + 1 099 511 627 776 + 549 755 813 888 + 274 877 906 944 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 0 + 0 + 0 + 536 870 912 + 0 + 134 217 728 + 0 + 0 + 16 777 216 + 8 388 608 + 0 + 0 + 0 + 0 + 0 + 0 + 65 536 + 32 768 + 0 + 0 + 4 096 + 0 + 0 + 0 + 0 + 0 + 64 + 0 + 0 + 8 + 4 + 0 + 1)(10) =

(4 611 686 018 427 387 904 + 2 305 843 009 213 693 952 + 1 152 921 504 606 846 976 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 72 057 594 037 927 936 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 9 007 199 254 740 992 + 4 503 599 627 370 496 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 562 949 953 421 312 + 281 474 976 710 656 + 140 737 488 355 328 + 70 368 744 177 664 + 35 184 372 088 832 + 17 592 186 044 416 + 8 796 093 022 208 + 4 398 046 511 104 + 2 199 023 255 552 + 1 099 511 627 776 + 549 755 813 888 + 274 877 906 944 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 536 870 912 + 134 217 728 + 16 777 216 + 8 388 608 + 65 536 + 32 768 + 4 096 + 64 + 8 + 4 + 1)(10) =

9 223 372 028 961 198 157(10)

5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:

0111 1111 1111 1111 1111 1111 1111 1110 0010 1001 1000 0001 1001 0000 0100 1101(2) = 9 223 372 028 961 198 157(10)

The signed binary number in one's complement representation 0111 1111 1111 1111 1111 1111 1111 1110 0010 1001 1000 0001 1001 0000 0100 1101(2) converted and written as an integer in decimal system (base ten):
0111 1111 1111 1111 1111 1111 1111 1110 0010 1001 1000 0001 1001 0000 0100 1101(2) = 9 223 372 028 961 198 157(10)

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

The signed binary in one's complement representation 0111 1111 1111 1111 1111 1111 1111 1110 0010 1001 1000 0001 1001 0000 0100 1100 converted and written as an integer number in decimal system (in base ten) = ?

The signed binary in one's complement representation 0111 1111 1111 1111 1111 1111 1111 1110 0010 1001 1000 0001 1001 0000 0100 1110 converted and written as an integer number in decimal system (in base ten) = ?

Convert signed binary numbers in one's complement representation to decimal system (base ten) integers

Binary number's length must be: 2, 4, 8, 16, 32, 64 - or else extra bits on 0 are added in front (to the left).

How to convert a signed binary number in one's complement representation to an integer in base ten:

1) In a signed binary one's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive.

2) Construct the unsigned binary number: flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s.

3) Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.

4) Add all the terms up to get the positive integer number in base ten.

5) Adjust the sign of the integer number by the first bit of the initial binary number.

The latest binary numbers in one's complement representation converted to signed integers numbers written in decimal system (base ten)

Convert signed binary number written in one's complement representation 0111 1111 1111 1111 1111 1111 1111 1110 0010 1001 1000 0001 1001 0000 0100 1101, write it as a decimal system (base ten) integer Nov 28 08:48 UTC (GMT)
Convert signed binary number written in one's complement representation 0010 1110 1011 1101, write it as a decimal system (base ten) integer Nov 28 08:47 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0000 0000 0000 1111 1111 1000 1110, write it as a decimal system (base ten) integer Nov 28 08:47 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0000 0000 0000 0001 0100 0110 0110 0010 1010 1011 0011 1100 1010 1110 0010, write it as a decimal system (base ten) integer Nov 28 08:46 UTC (GMT)
Convert signed binary number written in one's complement representation 0011 1001 0011 1001, write it as a decimal system (base ten) integer Nov 28 08:45 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 1011 0110 1010, write it as a decimal system (base ten) integer Nov 28 08:45 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0111 0010 0110, write it as a decimal system (base ten) integer Nov 28 08:44 UTC (GMT)
Convert signed binary number written in one's complement representation 1100 0110 1000 1000, write it as a decimal system (base ten) integer Nov 28 08:44 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0000 0000 0000 0001 0100 0110 0110 0010 1010 1011 0011 1100 1010 1100 1000, write it as a decimal system (base ten) integer Nov 28 08:44 UTC (GMT)
Convert signed binary number written in one's complement representation 1100 0001 1100 1011 1110 1001 1010 0000, write it as a decimal system (base ten) integer Nov 28 08:44 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0100 1110 1111 1111 1111 1110 1100, write it as a decimal system (base ten) integer Nov 28 08:44 UTC (GMT)
Convert signed binary number written in one's complement representation 1111 1101 0000 0010, write it as a decimal system (base ten) integer Nov 28 08:44 UTC (GMT)
Convert signed binary number written in one's complement representation 1100 1010 1111 1110 1010 1010 0001 1101, write it as a decimal system (base ten) integer Nov 28 08:44 UTC (GMT)
All the signed binary numbers in one's complement representation converted to decimal system (base ten) integers

How to convert signed binary numbers in one's complement representation from binary system to decimal

To understand how to convert a signed binary number in one's complement representation from binary system to decimal (base ten), the easiest way is to do it through an example - convert binary, 1001 1101, to base ten:

  • In a signed binary one's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive. The first bit is 1, so our number is negative.
  • Get the binary representation of the positive number, flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
    !(1001 1101) = 0110 0010
  • Write bellow the positive binary number representation in base two, and above each bit that makes up the binary number write the corresponding power of 2 (numeral base) that its place value represents, starting with zero, from the right of the number (rightmost bit), walking to the left of the number by increasing each corresonding power of 2 by exactly one unit:
  • powers of 2: 7 6 5 4 3 2 1 0
    digits: 0 1 1 0 0 0 1 0
  • Build the representation of the positive number in base 10, by taking each digit of the binary number, multiplying it by the corresponding power of 2 and then adding all the terms up:

    0110 0010(2) =

    (0 × 27 + 1 × 26 + 1 × 25 + 0 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 0 × 20)(10) =

    (0 + 64 + 32 + 0 + 0 + 0 + 2 + 0)(10) =

    (64 + 32 + 2)(10) =

    98(10)

  • Signed binary number in one's complement representation, 1001 1110 = -98(10), a signed negative integer in base 10